The adoption of Artificial intelligence (AI) technologies is steadily increasing. However, to become fully pervasive, AI needs resources at the edge of the network. The cloud can provide the processing power needed for big data, but edge computing is close to where data are produced and therefore crucial to their timely, flexible, and secure management. In this paper, we introduce the AI-SPRINT project, which will provide solutions to seamlessly design, partition, and run AI applications in computing continuum environments. AI-SPRINT will offer novel tools for AI applications development, secure execution, easy deployment, as well as runtime management and optimization: AI-SPRINT design tools will allow trading-off application performance (in terms of end-to-end latency or throughput), energy efficiency, and AI models accuracy while providing security and privacy guarantees. The runtime environment will support live data protection, architecture enhancement, agile delivery, runtime optimization, and continuous adaptation.